A class of superintegrable systems of Calogero type

TL;DR

This paper demonstrates that the three-body Calogero model with inverse square potentials is a maximally superintegrable and multiseparable system in three-dimensional Euclidean space, and it generalizes to a family of systems with arbitrary functions.

Contribution

It introduces a new perspective on the Calogero model as a superintegrable system and extends it to a broader family involving arbitrary functions.

Findings

Calogero model is maximally superintegrable in 3D

Model is multiseparable in Euclidean space

Generalization to systems with arbitrary functions

Abstract

We show that the three body Calogero model with inverse square potentials can be interpreted as a maximally superintegrable and multiseparable system in Euclidean three-space. As such it is a special case of a family of systems involving one arbitrary function of one variable.